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Group By... options are created in the XML definition of the Search view.

First, collect some information you will need:

Make sure you are in Developer
mode (1) and your user is in
the group Technical Features (2)

Navigate the menu sequence

Sales -> Customers

From the Debug View# menu, select Edit Search View

In the window that pops up, you can
see the definition of the base view,
including the <group> tag at the
bottom containing Salesperson,
Company and Country. (Technically you could edit this view, but the next time you upgraded the module, or upgraded the software, your edits would be overwritten)

Note the name of this view -
res.partner.select - and the object
is is defined for - res.partner -
and close the window.

Now, you need to make your own view that inherits the view you found and adds to it.

Navigate the menu sequence

Settings -> User Interface -> Views

Find any Search view, open it and click Duplicate from the More menu.

Name the view. Something like custom.res.partner.groupbystate for
example.

The Object is res.partner and the Inherited View is res.partner.select

Great answer, Ray. It's worth noting that if you want to group by a custom field **on a report** that does not exist in the report model, you will have to add it. See my gist where I add a field to the Group by... options for the Sales Analysis Report. https://gist.github.com/travs-w/f75719c0c33488da874333ac36ff4fe1

on the search box on the top right add you word to filter (the name of one of field displayed as a column in the tree or of table), you will have a list which propose you to do a search or a filter, choose filter, filter is done in the view, now you just have to save your filter to add it in the list, just click on the top right of the search box, on the right of "x" ( x is the button to delete your search), in section "personnal filter, give the name of filter and save just for you or for all users).